What is the derivative of y=x^8f(x) ?

The derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8

What is the first derivative of y=x^8f(x) ?

The first derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8

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derivative of

y = x^{8} f (x)

8 x^{7} f (x) + \frac{df}{d x} x^{8}

Solution steps

\frac{d}{d x} (x^{8} f (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{8}, g = f (x)

= \frac{d}{d x} (x^{8}) f (x) + \frac{df}{d x} x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

= 8 x^{7} f (x) + \frac{df}{d x} x^{8}

\int (1 + x)^{5} d x

x \to \infty lim (\frac{5 x}{5 x + 3 x ^{\frac{1}{x}}})

f (x) = 2 x - 3, 4, 0

f (x) = \frac{2}{x}, at x = 5

e^{3 x}

What is the derivative of y=x^8f(x) ?
The derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8
What is the first derivative of y=x^8f(x) ?
The first derivative of y=x^8f(x) is 8x^7f(x)+(df)/(dx)x^8